England's bowler Joe Root, left, celebrates the wicket of Indian batsman Parthiv Patel on the third day of the fourth cricket test match between India and England in Mumbai, India, Saturday, Dec. 10, 2016. (AP Photo/Rafiq Maqbool)

England’s attempts to fight back on day three of a fluctuating fourth Test foundered against India captain Virat Kohli’s exemplary second century of the series.

After Joe Root’s two wickets in four balls, India faltered to 307 for six from 262 for two in mid-afternoon, in reply to 400 all out at Mumbai’s Wankhede Stadium.

But Kohli (147no) escaped a sharp caught-and-bowled chance on 68 to Adil Rashid shortly afterwards and duly added his outstanding hundred to that of Murali Vijay (136) - the latter’s second of the series too - as the hosts took a first-innings lead, reaching stumps 451 for seven.

After Moeen Ali and Rashid eked out a wicket each, Root brought himself into the attack as the third spinner - while England captain Alastair Cook was briefly off the field - and nipped out Parthiv Patel and Ravi Ashwin.

He had given just one chance, a sharp stumping on 45 when he missed a Rashid googly the previous evening, but otherwise made no mistake with a measured balance between prolonged periods of defence and then strategic attack.

Nothing was happening for England, and Kohli was entirely untroubled throughout as he passed two more milestones in his prolific career - 1,000 Test runs this calendar year and then 4,000 in all.

But England’s hopes of reducing their series arrears to 2-1 began to flicker again after lunch.

The pitch played no part in Murali’s dismissal, but arguably the leg-spinner’s late dip did as he mistimed a low full toss back to a juggling Rashid.

Then Karun Nair went lbw, when Moeen found some telling turn at last and got his man lbw on review.

Parthiv had made his thoughts abundantly clear about England’s two frontline spinners when he described them at close-of-play on Friday as being “exposed”.

But he had not counted on Root, who needed only four deliveries to have him caught-behind trying to drive a perfectly-looped off-break - and then doubled up in his next over when Ashwin fell to a short-leg catch, Keaton Jennings standing his ground and grasping the ball as it stuck in his midriff.

England almost had the man they needed most - but Rashid could not hold on as a fierce blow back at him slid slightly off the face from a full leg-break and low to the bowler’s left.

Rashid continued a spell of 28 overs, spanning three sessions, and was rewarded when Ravindra Jadeja got underneath a big hit and was well-held by Jos Buttler running round from mid off to end a partnership of 57.

But Kohli was not done.

India crept into credit and - and after Jayant Yadav was put down by Root slightly to his left at second slip on eight when James Anderson took the long-delayed second new ball in the 130th over, they began to pile on England’s frustration in another telling stand of 87.

England’s mood could not have been helped when Jayant survived shortly before the close, after technology demonstrated he had edged Moeen behind down the leg side - but there was no option left to review the not-out decision because the two available had already been spent.

In this contest, much tighter than England’s previous two defeats, the cost of Rashid and Root’s drops was yet to be known in full.

But without them, it is fair to say the advantage might easily have been theirs rather than India’s.